Problem: Simplify the expression. $ (-5q^{5}+5q^{3}) - ( 5q^{7}-q^{4}) - ( -4q^{7}+6q^{5}) $
Solution: Distribute any negative signs. $(-5q^{5}+5q^{3}) + (-5q^{7}+q^{4}) + (4q^{7}-6q^{5})$ Since we are adding polynomials, we can simply remove the parentheses. $-5q^{5}+5q^{3} - 5q^{7}+q^{4} + 4q^{7}-6q^{5}$ Identify like terms. $ - \color{#DF0030}{5 q^5} + \color{#9D38BD}{5 q^3} - {5 q^7} + { q^4} + {4 q^7} - \color{#DF0030}{6 q^5} $ Combine like terms. $ { ( -5 + 4 ) q^7} + \color{#DF0030}{ q^5} + { q^4} + \color{#9D38BD}{ 5 q^3} $ Add the coefficients. $-q^{7}-11q^{5}+q^{4}+5q^{3}$